Search for your family name. Searches for names by County may be made free enabling you to find if they have a record of your surname. Further data will incur costs.
Family History Societies
There are many Family History Societies throughout the UK. The following sites will tell you about their work & will help you to locate the one that covers the area that you are researching. (Free site)
Initially for Birth /Marriage & Death certificates. (English & Welsh ) - but now greatly expanded Search for index numbers. (pay site but complete). To see a list of inclusions click here
This site, provided by the FamilyRecords.gov.uk consortium, will help you find the government records and other sources you need for your family history research.